Select the factors for the following expression 2x² - xy - 3y^2

Rationale

(2x-3y)(x+y)

To factor the expression 2x² - xy - 3y², we can identify two binomials that yield the original quadratic when multiplied. The correct factorization is (2x-3y)(x+y), as it expands back to the original expression.

A ((2x+3y)(x-y)) YOUR ANSWER

This choice expands to 2x² - 2xy + 3xy - 3y², which simplifies to 2x² + xy - 3y². The presence of the positive xy term indicates that this factorization does not yield the original expression.

B ((x+y)(2x-3y)) YOUR ANSWER

When expanded, this selection results in 2x² - 3xy + xy - 3y², simplifying to 2x² - 2xy - 3y². The negative coefficient of the xy term here does not match the original expression, confirming it as incorrect.

C ((2x-y)(x+3y)) YOUR ANSWER

This choice expands to 2x² + 6xy - xy - 3y², which simplifies to 2x² + 5xy - 3y². The presence of the positive 5xy term further confirms that this factorization does not represent the original expression accurately.

D ((2x-3y)(x+y)) CORRECT

This option correctly expands to 2x² + 2xy - 3y² - 3xy, which simplifies back to 2x² - xy - 3y², matching the original expression perfectly.

Conclusion

The correct factorization of the quadratic expression 2x² - xy - 3y² is (2x-3y)(x+y). Each incorrect choice fails to match the original expression upon expansion due to discrepancies in the coefficients of the xy term or incorrect constant terms. Understanding how to factor quadratics is crucial for solving polynomial equations and simplifying expressions effectively.

Select the factors for the following expression 2x² - xy - 3y^2

(2x-3y)(x+y)

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